Systems and methods for network-based biological activity assessment

Abstract

Systems and methods are disclosed herein for quantifying the response of a biological system to one or more perturbations based on measured activity data from a subset of the entities in the biological system. Based on the activity data and a network model of the biological system that describes the relationships between measured and non-measured entities, activities of entities that are not measured are inferred. The inferred activities are used for deriving a score quantifying the response of the biological system to a perturbation such as a response to a treatment condition. The score may be representative of the magnitude and topological distribution of the response of the network to the perturbation.

1 . A computerized method for quantifying perturbation of a biological system, comprising
 receiving, at a first processor, a first set of treatment data corresponding to a response of a first set of biological entities to a first treatment, wherein a first biological system comprises biological entities including the first set of biological entities and a second set of biological entities, each biological entity in the first biological system interacting with at least one other of the biological entities in the first biological system;   receiving, at a second processor, a second set of treatment data corresponding to a response of the first set of biological entities to a second treatment different from the first treatment;   providing, at a third processor, a first computational causal network model that represents the first biological system and includes:
 a first set of nodes representing the first set of biological entities, 
 a second set of nodes representing the second set of biological entities, 
 edges connecting nodes and representing relationships between the biological entities, and 
 direction values, representing an expected direction of change between the first treatment data and the second treatment data; 
   calculating, with a fourth processor, a first set of activity measures representing a difference between the first treatment data and the second treatment data for corresponding nodes in the first set of nodes;   generating, with a fifth processor, a second set of activity values for corresponding nodes in the second set of nodes, based on the first computational causal network model and the first set of activity measures.   
     
     
         2 . The method of  claim 1 , further comprising:
 generating, with a sixth processor, a score for the first computational causal network model representative of the perturbation of the first biological system to the first and second treatments based on the first computational causal network model and the second set of activity values.   
     
     
         3 . The method of  claim 1 , wherein generating the second set of activity values comprises identifying, for each particular node in the second set of nodes, an activity value that minimizes a difference statement that represents the difference between the activity value of the particular node and the activity value or activity measure of nodes to which the particular node is connected with an edge within the first computational causal network model, wherein the difference statement depends on the activity values of each node in the second set of nodes. 
     
     
         4 . The method of  claim 1 , wherein each activity value in the second set of activity values is a linear combination of activity measures of the first set of activity measures. 
     
     
         5 . The method of  claim 1 , further comprising providing a variation estimate for each activity value of the second set of activity values by forming a linear combination of variation estimates for each activity measure of the first set of activity measures. 
     
     
         6 . The method of  claim 2 , further comprising:
 representing the second set of activity values as a first activity value vector;   decomposing the first activity value vector into a first contributing vector and a first non-contributing vector, such that the sum of the first contributing and non-contributing vectors is the first activity value vector.   
     
     
         7 . The method of  claim 6 , wherein the first non-contributing vector is in a kernel of a quadratic function based on a signed Laplacian associated with the first computational causal network model. 
     
     
         8 . The method of  claim 6 , further comprising:
 receiving, at the first processor, a third set of treatment data corresponding to a response of the first set of biological entities to a third treatment;   receiving, at the second processor, a fourth set of treatment data corresponding to a response of the first set of biological entities to a fourth treatment;   calculating, with the fourth processor, a third set of activity measures corresponding to the first set of nodes, each activity measure in the third set of activity measures representing a difference between the third set of treatment data and the fourth set of treatment data for a corresponding node in the first set of nodes;   generating, with the fifth processor, a fourth set of activity values, each activity value representing an activity value for a corresponding node in the second set of nodes based on the first computational causal network model and the third set of activity measures;   representing the fourth set of activity values as a second activity value vector;   decomposing the second activity value vector into a second contributing vector and a second non-contributing vector, such that the sum of the second contributing and non-contributing vectors is the second activity value vector; and   comparing the first and second contributing vectors.   
     
     
         9 . The method of  claim 8 , wherein comparing the first and second contributing vectors comprises calculating a correlation between the first and second contributing vectors to indicate the comparability of the first and third sets of treatment data. 
     
     
         10 . The method of  claim 8 , wherein comparing the first and second contributing vectors comprises projecting the first and second contributing vectors onto an image space of a signed Laplacian of a computational network model. 
     
     
         11 . The method of  claim 1 , further comprising:
 receiving, at the first processor, a third set of treatment data corresponding to a response of a third set of biological entities to a third treatment different from the first treatment, wherein a second biological system comprises a plurality of biological entities including the third set of biological entities and a fourth set of biological entities, each biological entity in the second biological system interacting with at least one other of the biological entities in the second biological system;   receiving, at the second processor, a fourth set of treatment data corresponding to a response of the third set of biological entities to a fourth treatment different from the third treatment;   providing, at the third processor, a second computational causal network model that represents the second biological system and includes:
 a third set of nodes representing the third set of biological entities, 
 a fourth set of nodes representing the fourth set of biological entities, 
 edges connecting nodes and representing relationships between the biological entities, and 
 direction values, representing the expected direction of change between the third treatment data and the fourth treatment data; 
   calculating, with the fourth processor, a third set of activity measures corresponding to the third set of nodes, each activity measure in the third set of activity measures representing a difference between the third set of treatment data and the fourth set of treatment data for a corresponding node in the third set of nodes;   generating, with the fifth processor, a fourth set of activity values, each activity value representing an activity value for a corresponding node in the fourth set of nodes, based on the second computational causal network model and the third set of activity measures; and   comparing the fourth set of activity values to the second set of activity values.   
     
     
         12 . The method of  claim 11 , wherein comparing the fourth set of activity values to the second set of activity values comprises applying a kernel canonical correlation analysis based on a signed Laplacian associated with the first computational causal network model and a signed Laplacian associated with the second computational causal network model. 
     
     
         13 . The computerized method of  claim 1 , wherein the activity measure is a fold-change value, and the fold-change value for each node includes a logarithm of the difference between corresponding sets of treatment data for the biological entity represented by the respective node. 
     
     
         14 . The method of  claim 11 , wherein the first biological system and the second biological system are two different elements of the group consisting of an in vitro system, an in vivo system, a mouse system, a rat system, a non-human primate system and a human system. 
     
     
         15 . The method of  claim 1 , wherein:
 the first treatment data corresponds to the first biological system exposed to an agent; and   the second treatment data corresponds to the first biological system not exposed to the agent.   
     
     
         16 . The method of  claim 2 , further comprises determining the statistical significance of the score which is indicative of the perturbation of the biological system. 
     
     
         17 . The method of  claim 16 , wherein the statistical significance of the score is determined by comparing the score against a plurality of test scores each computed from a plurality of randomly-generated test computational causal network models.